The implementation and validation of the Chien low Reynolds number k-epsilon turbulence model in the two dimensional axisymmetric version Proteus, a compressible Navier-Stokes computer code, are presented. The set of k-epsilon equations are solved by marching in time using a coupled alternating direction implicit (ADI) solution procedure with generalized first or second order time differencing. To validate Proteus and the k-epsilon turbulence model, laminar and turbulent computations were done for several benchmark test cases: incompressible fully developed 2-D channel flow; fully developed axisymmetric pipe flow; boundary layer flow over a flat plate; and turbulent Sajben subsonic transonic diffuser flows. Proteus results from these test cases showed good agreement with analytical results and experimental data. Detailed comparisons of both mean flow and turbulent quantities showed that the Chien k-epsilon turbulence model given good results over a wider range of turbulent flow than the Baldwin-Lomax turbulence model in the Proteus code with no significant CPU time penalty for more complicated flow cases.